Problem: Simplify the following expression: $\dfrac{110x^4}{80x^4}$ You can assume $x \neq 0$.
Explanation: $ \dfrac{110x^4}{80x^4} = \dfrac{110}{80} \cdot \dfrac{x^4}{x^4} $ To simplify $\frac{110}{80}$ , find the greatest common factor (GCD) of $110$ and $80$ $110 = 2 \cdot 5 \cdot 11$ $80 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 5$ $ \mbox{GCD}(110, 80) = 2 \cdot 5 = 10 $ $ \dfrac{110}{80} \cdot \dfrac{x^4}{x^4} = \dfrac{10 \cdot 11}{10 \cdot 8} \cdot \dfrac{x^4}{x^4} $ $\phantom{ \dfrac{110}{80} \cdot \dfrac{4}{4}} = \dfrac{11}{8} \cdot \dfrac{x^4}{x^4} $ $ \dfrac{x^4}{x^4} = \dfrac{x \cdot x \cdot x \cdot x}{x \cdot x \cdot x \cdot x} = 1 $ $ \dfrac{11}{8} \cdot 1 = \dfrac{11}{8} $